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Excitation of the Electronic States of the Nitrogen Molecule by Electron Impact

1972; American Institute of Physics; Volume: 6; Issue: 3 Linguagem: Inglês

10.1103/physreva.6.988

0556-2791

Sang-Min Chung, Chun C. Lin,

Electron and X-Ray Spectroscopy Techniques

The electron-impact excitation cross sections of the $a^{1}\ensuremath{\Pi}_{g}$, ${c}^{\ensuremath{'}}^{1}\ensuremath{\Sigma}_{u}^{+}$, ${a}^{\ensuremath{'}\ensuremath{'}}^{1}\ensuremath{\Sigma}_{g}^{+}$, $w^{1}\ensuremath{\Delta}_{u}$, ${b}^{\ensuremath{'}}^{1}\ensuremath{\Sigma}_{u}^{+}$, $b^{1}\ensuremath{\Pi}_{u}$, $A^{3}\ensuremath{\Sigma}_{u}^{+}$, $B^{3}\ensuremath{\Pi}_{g}$, $C^{3}\ensuremath{\Pi}_{u}$, $D^{3}\ensuremath{\Sigma}_{u}^{+}$, $W^{3}\ensuremath{\Delta}_{u}$, and $E^{3}\ensuremath{\Sigma}_{g}^{+}$ states of ${\mathrm{N}}_{2}$ have been calculated over the range of 0-2000 eV for the singlet states and 0-40 eV for the triplet states by means of the Born approximation with Ochkur's and Rudge's scheme for treating the electron-exchange-scattering amplitude. The Franck-Condon-factor approximation was used to obtain the excitation cross sections to each vibrational level of the electronic states. The computation of the scattering-amplitude integrals was greatly facilitated by expressing the molecular wave functions in terms of atomic Gaussian-type orbitals. Four sets of self-consistent-field molecular wave functions have been employed for the calculations in order to test the sensitivity of the calculated cross sections to the choice of the wave functions. With the exception of the ${c}^{\ensuremath{'}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state, the cross sections based on three of the four sets vary by typically about 15%. As a test of the Born cross sections for singlet-singlet excitation, comparison between the theoretical and the available experimental values shows 25% agreement for the $a^{1}\ensuremath{\Pi}_{g}$ state at 900 eV and 50% for the ${a}^{\ensuremath{'}\ensuremath{'}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state at 80 eV. In the case of triplet excitation, the theoretical cross sections of the $C^{3}\ensuremath{\Pi}_{u}$ state agree very well with the experimental data, but for the $A^{3}\ensuremath{\Sigma}_{u}^{+}$ and $B^{3}\ensuremath{\Pi}_{g}$ states the discrepancy is generally as large as a factor of 2.